Talk:126/125

What it means for a superparticular ratio to be the difference between two others

Hello! I am wondering, what does it mean that a particular superparticular comma in a certain limit is the difference between two other superparticular commas in the same limit? Does it mean it has to be the mathematical quotient of two strictly larger commas than itself, or can one of them be smaller? E.g. 126/125 is the quotient of 81/80 and 225/224, but 225/224 is smaller than 126/125, so we might say this "doesn't count", we might say instead 225/224 is the difference between 81/80 and 126/125. This is natural and not too confusing. I discovered though that 126/125 is the quotient of 36/35 and 50/49, both of which are larger, so the previous information was nonetheless incorrect.

I don't suppose it's meaningful in any explicit ways. You may simply remove the part that's factually wrong. FloraC (talk) 09:59, 13 June 2021 (UTC)

Interestingly, if you go back in history, the sentence dates back to genewardsmith, see https://en.xen.wiki/index.php?title=126/125&diff=prev&oldid=4553 BTW: it started with consonances (instead of ratios) which might be less wrong... --Xenwolf (talk) 10:33, 13 June 2021 (UTC)

Ah, "consonances" rather than "superparticular ratios" make much more sense, however it wasn't true nonetheless, since 2401/2400 and 4375/4374 are also not the difference between any two 7-limit consonances, unless you count the septimal neutral thirds (49/40 and 60/49) or the subminor third resulting from stacking two 27/25 as "consonances", which is a bit of a stretch. I suppose we could stack 7/6 and 27/25 a bit, but it still wouldn't help getting two notably different consonances with these exact differences. The neutral third consonance is rather 11/9, for which 49/40 is merely an approximation (16/13 isn't as distinctly consonant although its inverse 13/8 actually is, since octave equivalence is only approximately correct in our direct perception). And 27/25 is rather an approximation for the two semiconsonances 13/12 and 14/13, which when stacked yields the true consonance 7/6 rather than a mere approximation (like (27/25)²). Henrik Ljungstrand (talk) 10:59, 13 June 2021 (UTC)